answer part a , b and c 4. (a) Find all solutions of the equation x²+2x+4=0 in Z.(b) Let R be a commutative ring with unity of characteristic 4. Compute and simplify(a+b)*.[24](d) Let R be a ring. Define what it means for R to be an integral domain.(c) Show that the matrixis a divisor of zero in M₂ (Z).

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Answered: 4. (a) Find all solutions of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 5E

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4. (a) Find all solutions of the equation x²+2x+4=0 in Z. (b) Let R be a commutative ring with unity of characteristic 4. Compute and simplify (a+b)* . (c) Show that the matrix [23 a divisor of zero in M₂ (Z). (d) Let R. be a ring. Define what it means for R to be an integral domain.